PROJECT SUMMARY Modern'health'monitoring'devices'at'hospitals'and'wearable'sensors'in'households'generate'a' large'amount'of'time'series'data'at'high'rate,'capturing'the'physiological'status'of'patients'in'a' real-time'fashion.'The'premise'is'that'these'technology'advances'enable'a'data-driven'healthcare' system' that' starts' making' fast,' accurate,' objective' and' inexpensive' decisions' based' upon' data,' in'addition'to'an'individual'physician?s'experience'and'preference.'However,'there'is'a'significant' gap' in' the' mathematical' theory' and' computational' tools' to' promptly' extract' actionable' information'from'multi-modal'non-stationary'time'series'data'in'a'robust'and'tractable'manner,' which' has' become' a' serious' roadblock' to' further' utilize' bigger' data' for' better' healthcare' monitoring.' The' goal' of' this' research' program' is' to' develop' a' mathematical' framework' for' extracting' time-frequency' and' geometric' representations' of' multi-modal' physiological' data,' in' an' online' and' robust' manner,' and' use' them' to' design' machine' learning' algorithms' to' improve' real-time' health' monitoring.' Specifically,' we' hypothesize' that' the' development' of' time-series' and' geometric' methods' for' large' streaming' multi-modal' monitoring' data' will' lead' to' more' accurate' diagnosis' on' various' physiological' monitoring' applications,' including' detection' and' prediction' of' rare' events' such' as' seizure' and' arrhythmia,' classification' of' sleep' stages' for' newborns'and'children,'and'real-time'artifact'removal'of'physiological'data.'To'achieve'our'goal,' we'plan'to'develop'novel'theoretical'and'computational'tools'for'analyzing'non-stationary'multi- modal' time' series' data' with' noise,' corruption' and' missing' data' as' well' as' real-time' algorithms' for' filtering' and' event' detection' from' such' data.' The' tools' and' algorithms' will' be' applied' on' clinical' tasks' at' the' Nationwide' Children's' Hospital.' In' addition,' the' real-time' workflow' will' be' implemented'on'Hadoop'clusters'with'a'mission'of'public'sharing'of'both'data'and'software.'The' development' from' the' interdisciplinary' team' composed' of' mathematicians,' biomedical' informaticians' as' well' as' the' hospital' will' not' only' transform' the' frontiers' of' mathematics' knowledge,' but' also' significantly' impact' clinical' applications,' data' science' education,' and' the' development'of'the'$110'billion'emerging'market'of'wireless'health.'' '